1. Field of the Invention
The present invention concerns a method of estimating the error occurring in the calculation of the spatial and temporal position of a mobile by a GPS (Global Positioning System) receiver.
2. Description of the Prior Art
The Global Positioning System is a well-known system for determining from the positions of a number of satellites, known at all times, the spatial and temporal position of a mobile provided with a GPS receiver capable of receiving and processing data from the satellites of the system which comprises 18 satellites in orbits such that most of the surface of the Earth can be "seen" by at least four satellites. At present up to nine satellites are used to determine the position of a mobile on the Earth but only four satellites are needed to determine the position of the mobile in time and in space in terms of four variables: x, y and z, the spatial coordinates of the mobile in a predetermined frame of reference, and its temporal coordinate (i.e. the date at which the mobile is at the calculated position, this date being specified in universal time).
The GPS receiver associated with a mobile includes means for:
selecting a set of four (or more) satellites visible from the point at which the mobile is located, and PA1 calculating the position of the mobile in time and space from data supplied by the selected satellites. PA1 A is the matrix: ##EQU1## .alpha..sub.ij, for i varying between 1 and 4 and j varying between 1 and 3, being the direction cosine of the angle between the jth coordinate axis and the straight line segment joining the mobile to the ith satellite and the subscripts 1, 2 and 3 being respectively associated with the abscissa, ordinate and third (z) axes, and PA1 Tr is the trace of the matrix (A.sup.T.A).sup.-1 i.e. the sum of its diagonal elements, A.sup.T is the transpose of the matrix A and (A.sup.T.A).sup.-1 is the inverse of the matrix A.sup.T.A. PA1 K is a matrix with N rows and four columns where N is the number of satellites in said constellation such that: ##EQU2## .alpha..sub.ij for i varying from 1 through N and j varying from 1 through 3 being the direction cosine of the angle between the jth coordinate axis and the straight line segment joining said mobile to the ith satellite of said constellation, the subscripts 1, 2 and 3 being respectively associated with the abscissa, ordinate and third axes, PA1 .epsilon..sub.r is a vector with N components URE.sub.1 through URE.sub.N where URE.sub.i for i varying from 1 through N is a datum supplied by said ith satellite giving the mean radial error between the theoretical position of said satellite and its actual position on the straight line segment joining said ith satellite to a point in the geographical area on the Earth seen by said ith satellite, the mean being calculated at the points of said geographical area at which a GPS ground station is located. PA1 a precision P is calculated from the components of .epsilon. by the equation: ##EQU3## P is compared with a predetermined tolerance threshold, and said GPS receiver selects another constellation if P is above said threshold.
The conventional GPS system offers 95% probability of a maximum error of 100 meters in the calculated horizontal position and 157 meters in the calculated vertical position. In other words, there is a 95% probability that the error in the horizontal position is 100 meters or less and the error in the vertical position is 157 meters or less. The GPS system guarantees a global accuracy which is a system constant.
A specific criterion for selecting the four satellites to be used by the GPS receiver to calculate the position of the mobile is used to select from all constellations (i.e. all sets) of four possible satellites from all the satellites in view that which can yield the guaranteed global accuracy of the GPS system in calculating the position of the mobile. This criterion C is proportional to .sqroot.Tr[(A.sup.T.A).sup.-1 ], where:
The coefficient of proportionality used to calculate C allows for all margins of inaccuracy of the GPS system. This constant coefficient therefore has a very high value for obvious reasons of security.
The criterion C is associated with a tolerance threshold and if this threshold is exceeded it is assumed that the corresponding constellation cannot guarantee the global accuracy; the GPS receiver then selects another constellation of four satellites and this process is repeated until the constellation yields an acceptable value of C.
Given the high value of the proportionality coefficient the criterion C is systematically penalized, i.e. a constellation may be rejected because it does not satisfy the global criterion C although in practise the accuracy with which it would enable the specific position to be calculated would be acceptable.
In some applications, for example construction of tunnels, installation of satellite antennas, sporting events and recreational sailing, for example, the GPS receiver can calculate the position of the mobile by integration over very long time periods so that the effects of the various sources of noise are minimized and the position finally calculated has an accuracy greater than the global accuracy guaranteed by the GPS system.
This is not possible in other applications, especially civil aviation. In this case it is not possible to wait for the system to integrate over a long time period. The accuracy achieved is then the guaranteed global accuracy, which is insufficient in the field of aviation. Likewise, the 5% inaccuracy is obviously intolerable in this field.
Consequently, given the hazards that it entails, the conventional GPS system is currently restricted to use in applications such that there is no great penalty in calculating the position of the mobile by integration over very long time periods.
The use of the criterion C is thus not only too constraining and penalizing but also insufficiently precise in many applications.
In military applications the GPS system uses a different transmission frequency than the conventional system. The data transmitted is encoded and cannot be decoded by a civilian user who does not have the appropriate decoder. In military applications the GPS system guarantees to a 95% probability a maximum error of 30 meters in all three dimensions. The criterion C employed is the same.
The guaranteed global accuracy and the use of the criterion C raise the same problems in military applications as use of the GPS system in civil applications.
Consideration might be given to estimating the error in the calculation of the position of the mobile by the GPS receiver. A method of this kind is described in the patent application JP-1 026 177, for example. The estimated measurement error, dependent on the calculated position, is obtained by multiplying the latter by a coefficient representing the degradation of the geometrical precision obtained with the GPS system (called GDOP, HDOP or PDOP in this system).
This coefficient is characteristic of the global inaccuracy margins of the GPS system. The error estimated by this method is therefore still a global error which is unsatisfactory in many applications and raises the same problems as the criterion C.
One object of the present invention is therefore to provide a method of supplying a conventional GPS system user with an estimate of the error in the calculated position which is more accurate than that produced by the prior art method.
Another object of the present invention is to enable more refined selection of the constellation of satellites to be used in calculating the position of a mobile.